Vascular dementia

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Vascular_dementia 

 

Vascular dementia
Other names	Arteriosclerotic dementia (in the ICD-9) Multi-infarct dementia (in the ICD-10) Vascular cognitive impairment
Specialty	Psychiatry, neurology
Symptoms	cognitive impairment

Vascular dementia (VaD) is dementia caused by problems in the supply of blood to the brain, typically a series of minor strokes, leading to worsening cognitive abilities, the decline occurring step by step. The term refers to a syndrome consisting of a complex interaction of cerebrovascular disease and risk factors that lead to changes in brain structures due to strokes and lesions, resulting in changes in cognition. The temporal relationship between a stroke and cognitive deficits is needed to make the diagnosis.

Signs and symptoms

Differentiating dementia syndromes can be challenging, due to the frequently overlapping clinical features and related underlying pathology. In particular, Alzheimer's disease often co-occurs with vascular dementia.

People with vascular dementia present with progressive cognitive impairment, acutely or sub-acutely as in mild cognitive impairment, frequently step-wise, after multiple cerebrovascular events (strokes). Some people may appear to improve between events and decline after further silent strokes. A rapidly deteriorating condition may lead to death from a stroke, heart disease, or infection.

The disease is described as both a mental disorder and behavioural disorder within the International Classification of Diseases. Signs and symptoms are cognitive, motor, behavioral, and for a significant proportion of patients, also affective. These changes typically occur over a period of 5–10 years. Signs are typically the same as in other dementias, but mainly include cognitive decline and memory impairment of sufficient severity as to interfere with activities of daily living, sometimes with presence of focal neurologic signs, and evidence of features consistent with cerebrovascular disease on brain imaging (CT or MRI). The neurologic signs localizing to certain areas of the brain that can be observed are hemiparesis, bradykinesia, hyperreflexia, extensor plantar reflexes, ataxia, pseudobulbar palsy, as well as gait problems and swallowing difficulties. People have patchy deficits in terms of cognitive testing. They tend to have better free recall and fewer recall intrusions when compared with patients with Alzheimer's disease. In the more severely affected patients, or patients affected by infarcts in Wernicke's or Broca's areas, specific problems with speaking called dysarthria and aphasias may be present.

In small vessel disease, the frontal lobes are often affected. Consequently, patients with vascular dementia tend to perform worse than their Alzheimer's disease counterparts in frontal lobe tasks, such as verbal fluency, and may present with frontal lobe problems: apathy, abulia (lack of will or initiative), problems with attention, orientation, and urinary incontinence. They tend to exhibit more perseverative behavior. VaD patients may also present with general slowing of processing ability, difficulty shifting sets, and impairment in abstract thinking. Apathy early in the disease is more suggestive of vascular dementia.

Rare genetic disorders that cause vascular lesions in the brain have other presentation patterns. As a rule, they tend to occur earlier in life and have a more aggressive course. In addition, infectious disorders, such as syphilis, can cause arterial damage, strokes, and bacterial inflammation of the brain.

Causes

Vascular dementia can be caused by ischemic or hemorrhagic infarcts affecting multiple brain areas, including the anterior cerebral artery territory, the parietal lobes, or the cingulate gyrus. On rare occasion, infarcts in the hippocampus or thalamus are the cause of dementia. A history of stroke increases the risk of developing dementia by around 70%, and recent stroke increases the risk by around 120%. Brain vascular lesions can also be the result of diffuse cerebrovascular disease, such as small vessel disease.

Risk factors for vascular dementia include age, hypertension, smoking, hypercholesterolemia, diabetes mellitus, cardiovascular disease, and cerebrovascular disease. Other risk factors include geographic origin, genetic predisposition, and prior strokes.

Vascular dementia can sometimes be triggered by cerebral amyloid angiopathy, which involves accumulation of beta amyloid plaques in the walls of the cerebral arteries, leading to breakdown and rupture of the vessels. Since amyloid plaques are a characteristic feature of Alzheimer's disease, vascular dementia may occur as a consequence. Cerebral amyloid angiopathy can, however, appear in people with no prior dementia condition. Amyloid beta accumulation is often present in cognitively normal elderly people.

Two reviews of 2018 and 2019 found potentially an association between celiac disease and vascular dementia.

Diagnosis

Several specific diagnostic criteria can be used to diagnose vascular dementia, including the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV) criteria, the International Classification of Diseases, Tenth Edition (ICD-10) criteria, the National Institute of Neurological Disorders and Stroke criteria, Association Internationale pour la Recherche et l'Enseignement en Neurosciences (NINDS-AIREN) criteria, the Alzheimer's Disease Diagnostic and Treatment Center criteria, and the Hachinski Ischemic Score (after Vladimir Hachinski).

The recommended investigations for cognitive impairment include: blood tests (for anemia, vitamin deficiency, thyrotoxicosis, infection, etc.), chest X-Ray, ECG, and neuroimaging, preferably a scan with a functional or metabolic sensitivity beyond a simple CT or MRI. When available as a diagnostic tool, single photon emission computed tomography (SPECT) and positron emission tomography (PET) neuroimaging may be used to confirm a diagnosis of multi-infarct dementia in conjunction with evaluations involving mental status examination. In a person already having dementia, SPECT appears to be superior in differentiating multi-infarct dementia from Alzheimer's disease, compared to the usual mental testing and medical history analysis. Advances have led to the proposal of new diagnostic criteria.

The screening blood tests typically include full blood count, liver function tests, thyroid function tests, lipid profile, erythrocyte sedimentation rate, C reactive protein, syphilis serology, calcium serum level, fasting glucose, urea, electrolytes, vitamin B-12, and folate. In selected patients, HIV serology and certain autoantibody testing may be done.

Mixed dementia is diagnosed when people have evidence of Alzheimer's disease and cerebrovascular disease, either clinically or based on neuro-imaging evidence of ischemic lesions.

Pathology

Gross examination of the brain may reveal noticeable lesions and damage to blood vessels. Accumulation of various substances such as lipid deposits and clotted blood appear on microscopic views. The white matter is most affected, with noticeable atrophy (tissue loss), in addition to calcification of the arteries. Microinfarcts may also be present in the gray matter (cerebral cortex), sometimes in large numbers. Although atheroma of the major cerebral arteries is typical in vascular dementia, smaller vessels and arterioles are mainly affected.

Prevention

Early detection and accurate diagnosis are important, as vascular dementia is at least partially preventable. Ischemic changes in the brain are irreversible, but the patient with vascular dementia can demonstrate periods of stability or even mild improvement. Since stroke is an essential part of vascular dementia, the goal is to prevent new strokes. This is attempted through reduction of stroke risk factors, such as high blood pressure, high blood lipid levels, atrial fibrillation, or diabetes mellitus. Meta-analyses have found that medications for high blood pressure are effective at prevention of pre-stroke dementia, which means that high blood pressure treatment should be started early. These medications include angiotensin converting enzyme inhibitors, diuretics, calcium channel blockers, sympathetic nerve inhibitors, angiotensin II receptor antagonists or adrenergic antagonists. Elevated lipid levels, including HDL, were found to increase risk of vascular dementia. However, six large recent reviews showed that therapy with statin drugs was ineffective in treatment or prevention of this dementia. Aspirin is a medication that is commonly prescribed for prevention of strokes and heart attacks; it is also frequently given to patients with dementia. However, its efficacy in slowing progression of dementia or improving cognition has not been supported by studies. Smoking cessation and Mediterranean diet have not been found to help patients with cognitive impairment; physical activity was consistently the most effective method of preventing cognitive decline.

Treatment

Currently, there are no medications that have been approved specifically for prevention or treatment of vascular dementia. The use of medications for treatment of Alzheimer's dementia, such as cholinesterase inhibitors and memantine, has shown small improvement of cognition in vascular dementia. This is most likely due to the drugs' actions on co-existing AD-related pathology. Multiple studies found a small benefit in VaD treatment with: memantine, a non-competitive N-methyl-D-aspartate (NMDA) receptor antagonist; cholinesterase inhibitors galantamine, donepezil, rivastigmine; Studies have shown that an extract of Ginkgo biloba EGb761 improves cognition, daily activities, and quality of life in treating vascular dementia, and is seen to be effective regardless of the severity of symptoms.

In those with celiac disease or non-celiac gluten sensitivity, a strict gluten-free diet may relieve symptoms of mild cognitive impairment. It should be started as soon as possible. There is no evidence that a gluten free diet is useful against advanced dementia. People with no digestive symptoms are less likely to receive early diagnosis and treatment.

General management of dementia includes referral to community services, aid with judgment and decision-making regarding legal and ethical issues (e.g., driving, capacity, advance directives), and consideration of caregiver stress. Behavioral and affective symptoms deserve special consideration in this patient group. These problems tend to resist conventional psychopharmacological treatment, and often lead to hospital admission and placement in permanent care.

Prognosis

Many studies have been conducted to determine average survival of patients with dementia. The studies were frequently small and limited, which caused contradictory results in the connection of mortality to the type of dementia and the patient's gender. A very large study conducted in Netherlands in 2015 found that the one-year mortality was three to four times higher in patients after their first referral to a day clinic for dementia, when compared to the general population. If the patient was hospitalized for dementia, the mortality was even higher than in patients hospitalized for cardiovascular disease. Vascular dementia was found to have either comparable or worse survival rates when compared to Alzheimer's Disease; another very large 2014 Swedish study found that the prognosis for VaD patients was worse for male and older patients.

Unlike Alzheimer's disease, which weakens the patient, causing them to succumb to bacterial infections like pneumonia, vascular dementia can be a direct cause of death due to the possibility of a fatal interruption in the brain's blood supply.

Epidemiology

Vascular dementia is the second-most-common form of dementia after Alzheimer's disease (AD) in older adults. The prevalence of the illness is 1.5% in Western countries and approximately 2.2% in Japan. It accounts for 50% of all dementias in Japan, 20% to 40% in Europe and 15% in Latin America. 25% of stroke patients develop new-onset dementia within one year of their stroke. One study found that in the United States, the prevalence of vascular dementia in all people over the age of 71 is 2.43%, and another found that the prevalence of the dementias doubles with every 5.1 years of age. The incidence peaks between the fourth and the seventh decades of life and 80% of patients have a history of hypertension.

A recent meta-analysis identified 36 studies of prevalent stroke (1.9 million participants) and 12 studies of incident stroke (1.3 million participants). For prevalent stroke, the pooled hazard ratio for all-cause dementia was 1.69 (95% confidence interval: 1.49–1.92; P < .00001; I² = 87%). For incident stroke, the pooled risk ratio was 2.18 (95% confidence interval: 1.90–2.50; P < .00001; I² = 88%). Study characteristics did not modify these associations, with the exception of sex, which explained 50.2% of between-study heterogeneity for prevalent stroke. These results confirm that stroke is a strong, independent, and potentially modifiable risk factor for all-cause dementia.

Turtles all the way down

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Turtles_all_the_way_down 

The saying holds that the world is supported by a chain of increasingly large turtles. Beneath each turtle is yet another: it is "turtles all the way down".

"Turtles all the way down" is an expression of the problem of infinite regress. The saying alludes to the mythological idea of a World Turtle that supports a flat Earth on its back. It suggests that this turtle rests on the back of an even larger turtle, which itself is part of a column of increasingly large turtles that continues indefinitely.

The exact origin of the phrase is uncertain. In the form "rocks all the way down", the saying appears as early as 1838. References to the saying's mythological antecedents, the World Turtle and its counterpart the World Elephant, were made by a number of authors in the 17th and 18th centuries.

The expression has been used to illustrate problems such as the regress argument in epistemology.

History

Background in Hindu mythology

Further information: World Turtle and World Elephant

Four World Elephants resting on a World Turtle

Early variants of the saying do not always have explicit references to infinite regression (i.e., the phrase "all the way down"). They often reference stories featuring a World Elephant, World Turtle, or other similar creatures that are claimed to come from Hindu mythology. The first known reference to a Hindu source is found in a letter by Jesuit Emanuel da Veiga (1549–1605), written at Chandagiri on 18 September 1599, in which the relevant passage reads:

Alii dicebant terram novem constare angulis, quibus cœlo innititur. Alius ab his dissentiens volebat terram septem elephantis fulciri, elephantes uero ne subsiderent, super testudine pedes fixos habere. Quærenti quis testudinis corpus firmaret, ne dilaberetur, respondere nesciuit.

Others hold that the earth has nine corners by which the heavens are supported. Another disagreeing from these would have the earth supported by seven elephants, and the elephants do not sink down because their feet are fixed on a tortoise. When asked who would fix the body of the tortoise, so that it would not collapse, he said that he did not know.

Veiga's account seems to have been received by Samuel Purchas, who has a close paraphrase in his Purchas His Pilgrims (1613/1626), "that the Earth had nine corners, whereby it was borne up by the Heaven. Others dissented, and said, that the Earth was borne up by seven Elephants; the Elephants' feet stood on Tortoises, and they were borne by they know not what." Purchas' account is again reflected by John Locke in his 1689 tract An Essay Concerning Human Understanding, where Locke introduces the story as a trope referring to the problem of induction in philosophical debate. Locke compares one who would say that properties inhere in "Substance" to the Indian who said the world was on an elephant which was on a tortoise, "But being again pressed to know what gave support to the broad-back'd Tortoise, replied, something, he knew not what". The story is also referenced by Henry David Thoreau, who writes in his journal entry of 4 May 1852: "Men are making speeches ... all over the country, but each expresses only the thought, or the want of thought, of the multitude. No man stands on truth. They are merely banded together as usual, one leaning on another and all together on nothing; as the Hindoos made the world rest on an elephant, and the elephant on a tortoise, and had nothing to put under the tortoise."

Modern form

In the form of "rocks all the way down", the saying dates to at least 1838, when it was printed in an unsigned anecdote in the New-York Mirror about a schoolboy and an old woman living in the woods:

"The world, marm," said I, anxious to display my acquired knowledge, "is not exactly round, but resembles in shape a flattened orange; and it turns on its axis once in twenty-four hours."

"Well, I don't know anything about its axes," replied she, "but I know it don't turn round, for if it did we'd be all tumbled off; and as to its being round, any one can see it's a square piece of ground, standing on a rock!"

"Standing on a rock! but upon what does that stand?"

"Why, on another, to be sure!"

"But what supports the last?"

"Lud! child, how stupid you are! There's rocks all the way down!"

A version of the saying in its "turtle" form appeared in an 1854 transcript of remarks by preacher Joseph Frederick Berg addressed to Joseph Barker:

My opponent's reasoning reminds me of the heathen, who, being asked on what the world stood, replied, "On a tortoise." But on what does the tortoise stand? "On another tortoise." With Mr. Barker, too, there are tortoises all the way down. (Vehement and vociferous applause.)

— "Second Evening: Remarks of Rev. Dr. Berg"

William James

Many 20th-century attributions claim that philosopher and psychologist William James is the source of the phrase. James referred to the fable of the elephant and tortoise several times, but told the infinite regress story with "rocks all the way down" in his 1882 essay, "Rationality, Activity and Faith":

Like the old woman in the story who described the world as resting on a rock, and then explained that rock to be supported by another rock, and finally when pushed with questions said it was "rocks all the way down," he who believes this to be a radically moral universe must hold the moral order to rest either on an absolute and ultimate should or on a series of shoulds "all the way down."

The linguist John R. Ross also associates James with the phrase:

The following anecdote is told of William James. [...] After a lecture on cosmology and the structure of the solar system, James was accosted by a little old lady.

"Your theory that the sun is the centre of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr. James, but it's wrong. I've got a better theory," said the little old lady.

"And what is that, madam?" inquired James politely.

"That we live on a crust of earth which is on the back of a giant turtle."

Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of her position.

"If your theory is correct, madam," he asked, "what does this turtle stand on?"

"You're a very clever man, Mr. James, and that's a very good question," replied the little old lady, "but I have an answer to it. And it's this: The first turtle stands on the back of a second, far larger, turtle, who stands directly under him."

"But what does this second turtle stand on?" persisted James patiently.

To this, the little old lady crowed triumphantly,

"It's no use, Mr. James—it's turtles all the way down."

— J. R. Ross, Constraints on Variables in Syntax, 1967

Turtle world, infinite regress and explanatory failure

The mythological idea of a turtle world is often used as an illustration of infinite regresses. An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. The main interest in infinite regresses is due to their role in infinite regress arguments. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. There are different ways how a regress can be vicious. The idea of a turtle world exemplifies viciousness due to explanatory failure: it does not solve the problem it was formulated to solve. Instead, it assumes already in disguised form what it was supposed to explain. This is akin to the informal fallacy of begging the question. On one interpretation, the goal of positing the existence of a world turtle is to explain why the earth seems to be at rest instead of falling down: because it rests on the back of a giant turtle. In order to explain why the turtle itself is not in free fall, another even bigger turtle is posited and so on, resulting in a world that is turtles all the way down. Despite its shortcomings in clashing with modern physics and due to its ontological extravagance, this theory seems to be metaphysically possible assuming that space is infinite, thereby avoiding an outright contradiction. But it fails because it has to assume rather than explain at each step that there is another thing that is not falling. It does not explain why nothing at all is falling.

In epistemology and other disciplines

The metaphor is used as an example of the problem of infinite regress in epistemology to show that there is a necessary foundation to knowledge, as written by Johann Gottlieb Fichte in 1794:

"If there is not to be any (system of human knowledge dependent upon an absolute first principle) two cases are only possible. Either there is no immediate certainty at all, and then our knowledge forms many series or one infinite series, wherein each theorem is derived from a higher one, and this again from a higher one, etc., etc. We build our houses on the earth, the earth rests on an elephant, the elephant on a tortoise, the tortoise again--who knows on what?-- and so on ad infinitum. True, if our knowledge is thus constituted, we can not alter it; but neither have we, then, any firm knowledge. We may have gone back to a certain link of our series, and have found every thing firm up to this link; but who can guarantee us that, if we go further back, we may not find it ungrounded, and shall thus have to abandon it? Our certainty is only assumed, and we can never be sure of it for a single following day."

David Hume references the story in his Dialogues Concerning Natural Religion when arguing against God as an unmoved mover:

How, therefore, shall we satisfy ourselves concerning the cause of that Being whom you suppose the Author of Nature, or, according to your system of Anthropomorphism, the ideal world, into which you trace the material? Have we not the same reason to trace that ideal world into another ideal world, or new intelligent principle? But if we stop, and go no further; why go so far? why not stop at the material world? How can we satisfy ourselves without going on in infinitum? And, after all, what satisfaction is there in that infinite progression? Let us remember the story of the Indian philosopher and his elephant. It was never more applicable than to the present subject. If the material world rests upon a similar ideal world, this ideal world must rest upon some other; and so on, without end. It were better, therefore, never to look beyond the present material world. By supposing it to contain the principle of its order within itself, we really assert it to be God; and the sooner we arrive at that Divine Being, so much the better. When you go one step beyond the mundane system, you only excite an inquisitive humour which it is impossible ever to satisfy.

Bertrand Russell also mentions the story in his 1927 lecture Why I Am Not a Christian while discounting the First Cause argument intended to be a proof of God's existence:

If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. It is exactly of the same nature as the Hindu's view, that the world rested upon an elephant and the elephant rested upon a tortoise; and when they said, 'How about the tortoise?' the Indian said, 'Suppose we change the subject.'

Notable modern allusions or variations

References to "turtles all the way down" have been made in a variety of modern contexts. For example, "Turtles All the Way Down" is the name of a song by country artist Sturgill Simpson that appears on his 2014 album Metamodern Sounds in Country Music. "Gamma Goblins ('Its Turtles All The Way Down' Mix)" is a remix by Ott for the 2002 Hallucinogen album In Dub. Turtles All the Way Down is also the title of a 2017 novel by John Green about a teenage girl with obsessive–compulsive disorder.

Stephen Hawking incorporates the saying into the beginning of his 1988 book A Brief History of Time:

A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the centre of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!"

Justice Antonin Scalia of the U.S. Supreme Court discussed his "favored version" of the saying in a footnote to his plurality opinion in Rapanos v. United States:

In our favored version, an Eastern guru affirms that the earth is supported on the back of a tiger. When asked what supports the tiger, he says it stands upon an elephant; and when asked what supports the elephant he says it is a giant turtle. When asked, finally, what supports the giant turtle, he is briefly taken aback, but quickly replies "Ah, after that it is turtles all the way down."

Microsoft Visual Studio had a gamification plug-in that awarded badges for certain programming behaviors and patterns. One of the badges was "Turtles All the Way Down", which was awarded for writing a class with 10 or more levels of inheritance.

American rock band mewithoutYou titled a song "Tortoises All the Way Down," as a play on this image, on their 2018 album [Untitled].

In Terry Pratchett's Discworld the flat planet is balanced on the backs of four elephants which in turn stand on the back of a giant turtle.

In World of Warcraft, "Turtles All The Way Down" is the name of an achievement for acquiring a Sea Turtle mount.

In Final Fantasy XV, after the party defeats the Adamantoise, a turtle that is the size of a mountain, Ignis quips that "the turtle's all the way down."

In Borderlands, graffiti "Turtles all the way down" can be found inside a shed opposite the entrance to the Titan bandit camp in Arid Badlands.

Infinite regress

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Infinite_regress

An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. In the epistemic regress, for example, a belief is justified because it is based on another belief that is justified. But this other belief is itself in need of one more justified belief for itself to be justified and so on. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. There are different ways how a regress can be vicious. The most serious form of viciousness involves a contradiction in the form of metaphysical impossibility. Other forms occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve. Traditionally, it was often assumed without much argument that each infinite regress is vicious but this assumption has been put into question in contemporary philosophy. While some philosophers have explicitly defended theories with infinite regresses, the more common strategy has been to reformulate the theory in question in a way that avoids the regress. One such strategy is foundationalism, which posits that there is a first element in the series from which all the other elements arise but which is not itself explained this way. Another way is coherentism, which is based on a holistic explanation that usually sees the entities in question not as a linear series but as an interconnected network. Infinite regress arguments have been made in various areas of philosophy. Famous examples include the cosmological argument, Bradley's regress and regress arguments in epistemology.

Definition

An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. This principle can often be expressed in the following form: X is F because X stands in R to Y and Y is F. X and Y stand for objects, R stands for a relation and F stands for a property in the widest sense. In the epistemic regress, for example, a belief is justified because it is based on another belief that is justified. But this other belief is itself in need of one more justified belief for itself to be justified and so on. Or in the cosmological argument, an event occurred because it was caused by another event that occurred before it, which was itself caused by a previous event, and so on. This principle by itself is not sufficient: it does not lead to a regress if there is no X that is F. This is why an additional triggering condition has to be fulfilled: there has to be an X that is F for the regress to get started. So the regress starts with the fact that X is F. According to the recursive principle, this is only possible if there is a distinct Y that is also F. But in order to account for the fact that Y is F, we need to posit a Z that is F and so on. Once the regress has started, there is no way of stopping it since a new entity has to be introduced at each step in order to make the previous step possible.

An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. The mere existence of an infinite regress by itself is not a proof for anything. So in addition to connecting the theory to a recursive principle paired with a triggering condition, the argument has to show in which way the resulting regress is vicious. For example, one form of evidentialism in epistemology holds that a belief is only justified if it is based on another belief that is justified. An opponent of this theory could use an infinite regress argument by demonstrating (1) that this theory leads to an infinite regress (e.g. by pointing out the recursive principle and the triggering condition) and (2) that this infinite regress is vicious (e.g. by showing that it is implausible given the limitations of the human mind). In this example, the argument has a negative form since it only denies that another theory is true. But it can also be used in a positive form to support a theory by showing that its alternative involves a vicious regress. This is how the cosmological argument for the existence of God works: it claims that positing God's existence is necessary in order to avoid an infinite regress of causes.

Viciousness

For an infinite regress argument to be successful, it has to show that the involved regress is vicious. A non-vicious regress is called virtuous or benign. Traditionally, it was often assumed without much argument that each infinite regress is vicious but this assumption has been put into question in contemporary philosophy. In most cases, it is not self-evident whether an infinite regress is vicious or not. The truth regress constitutes an example of an infinite regress that is not vicious: if the proposition "P" is true, then the proposition that "It is true that P" is also true and so on. Infinite regresses pose a problem mostly if the regress concerns concrete objects. Abstract objects, on the other hand, are often considered to be unproblematic in this respect. For example, the truth-regress leads to an infinite number of true propositions or the Peano axioms entail the existence of infinitely many natural numbers. But these regresses are usually not held against the theories that entail them.

There are different ways how a regress can be vicious. The most serious type of viciousness involves a contradiction in the form of metaphysical impossibility. Other types occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve. The vice of an infinite regress can be local if it causes problems only for certain theories when combined with other assumptions, or global otherwise. For example, an otherwise virtuous regress is locally vicious for a theory that posits a finite domain. In some cases, an infinite regress is not itself the source of the problem but merely indicates a different underlying problem.

Impossibility

Infinite regresses that involve metaphysical impossibility are the most serious cases of viciousness. The easiest way to arrive at this result is by accepting the assumption that actual infinities are impossible, thereby directly leading to a contradiction. This anti-infinitists position is opposed to infinity in general, not just specifically to infinite regresses. But it is open to defenders of the theory in question to deny this outright prohibition on actual infinities. For example, it has been argued that only certain types of infinities are problematic in this way, like infinite intensive magnitudes (e.g. infinite energy densities). But other types of infinities, like infinite cardinality (e.g. infinitely many causes) or infinite extensive magnitude (e.g. the duration of the universe's history) are unproblematic from the point of view of metaphysical impossibility. While there may be some instances of viciousness due to metaphysical impossibility, most vicious regresses are problematic because of other reasons.

Implausibility

A more common form of viciousness arises from the implausibility of the infinite regress in question. This category often applies to theories about human actions, states or capacities. This argument is weaker than the argument from impossibility since it allows that the regress in question is possible. It only denies that it is actual. For example, it seems implausible due to the limitations of the human mind that there are justified beliefs if this entails that the agent needs to have an infinite amount of them. But this is not metaphysically impossible, e.g. if it is assumed that the infinite number of beliefs are only non-occurrent or dispositional while the limitation only applies to the number of beliefs one is actually thinking about at one moment. Another reason for the implausibility of theories involving an infinite regress is due to the principle known as Ockham's razor, which posits that we should avoid ontological extravagance by not multiplying entities without necessity. Considerations of parsimony are complicated by the distinction between quantitative and qualitative parsimony: concerning how many entities are posited in contrast to how many kinds of entities are posited. For example, the cosmological argument for the existence of God promises to increase quantitative parsimony by positing that there is one first cause instead of allowing an infinite chain of events. But it does so by decreasing qualitative parsimony: it posits God as a new type of entity.

Failure to explain

Another form of viciousness applies not to the infinite regress by itself but to it in relation to the explanatory goals of a theory. Theories are often formulated with the goal of solving a specific problem, e.g. of answering the question why a certain type of entity exists. One way how such an attempt can fail is if the answer to the question already assumes in disguised form what it was supposed to explain. This is akin to the informal fallacy of begging the question. From the perspective of a mythological world view, for example, one way to explain why the earth seems to be at rest instead of falling down is to hold that it rests on the back of a giant turtle. In order to explain why the turtle itself is not in free fall, another even bigger turtle is posited and so on, resulting in a world that is turtles all the way down. Despite its shortcomings in clashing with modern physics and due to its ontological extravagance, this theory seems to be metaphysically possible assuming that space is infinite. One way to assess the viciousness of this regress is to distinguish between local and global explanations. A local explanation is only interested in explaining why one thing has a certain property through reference to another thing without trying to explain this other thing as well. A global explanation, on the other hand, tries to explain why there are any things with this property at all. So as a local explanation, the regress in the turtle theory is benign: it succeeds in explaining why the earth is not falling. But as a global explanation, it fails because it has to assume rather than explain at each step that there is another thing that is not falling. It does not explain why nothing at all is falling.

It has been argued that infinite regresses can be benign under certain circumstances despite aiming at global explanation. This line of thought rests on the idea of the transmission involved in the vicious cases: it is explained that X is F because Y is F where this F was somehow transmitted from Y to X. The problem is that to transfer something, you have to possess it first, so the possession is presumed rather than explained. For example, assume that in trying to explain why your neighbor has the property of being the owner of a bag of sugar, it is revealed that this bag was first in someone else's possession before it was transferred to your neighbor and that the same is true for this and every other previous owner. This explanation is unsatisfying since ownership is presupposed at every step. In non-transmissive explanations, on the other hand, Y is still the reason for X being F and Y is also F but this is just seen as a contingent fact. This line of thought has been used to argue that the epistemic regress is not vicious. From a Bayesian point of view, for example, justification or evidence can be defined in terms of one belief raising the probability that another belief is true. The former belief may also be justified but this is not relevant for explaining why the latter belief is justified.

Responses to infinite regress arguments

Philosophers have responded to infinite regress arguments in various ways. The criticized theory can be defended, for example, by denying that an infinite regress is involved. Infinitists, on the other hand, embrace the regress but deny that it is vicious. Another response is to modify the theory in order to avoid the regress. This can be achieved in the form of foundationalism or of coherentism.

Foundationalism

Traditionally, the most common response is foundationalism. It posits that there is a first element in the series from which all the other elements arise but which is not itself explained this way. So from any given position, the series can be traced back to elements on the most fundamental level, which the recursive principle fails to explain. This way an infinite regress is avoided. This position is well-known from its applications in the field of epistemology. Foundationalist theories of epistemic justification state that besides inferentially justified beliefs, which depend for their justification on other beliefs, there are also non-inferentially justified beliefs. The non-inferentially justified beliefs constitute the foundation on which the superstructure consisting of all the inferentially justified beliefs rests. Acquaintance theories, for example, explain the justification of non-inferential beliefs through acquaintance with the objects of the belief. On such a view, an agent is inferentially justified to believe that it will rain tomorrow based on the belief that the weather forecast told so. She is non-inferentially justified in believing that she is in pain because she is directly acquainted with the pain. So a different type of explanation (acquaintance) is used for the foundational elements.

Another example comes from the field of metaphysics concerning the problem of ontological hierarchy. One position in this debate claims that some entities exist on a more fundamental level than other entities and that the latter entities depend on or are grounded in the former entities. Metaphysical foundationalism is the thesis that these dependence relations do not form an infinite regress: that there is a most fundamental level that grounds the existence of the entities from all other levels. This is sometimes expressed by stating that the grounding-relation responsible for this hierarchy is well-founded.^[15]

Coherentism

Coherentism, mostly found in the field of epistemology, is another way to avoid infinite regresses. It is based on a holistic explanation that usually sees the entities in question not as a linear series but as an interconnected network. For example, coherentist theories of epistemic justification hold that beliefs are justified because of the way they hang together: they cohere well with each other. This view can be expressed by stating that justification is primarily a property of the system of beliefs as a whole. The justification of a single belief is derivative in the sense that it depends on the fact that this belief belongs to a coherent whole. Laurence BonJour is a well-known contemporary defender of this position.

Examples

Aristotle

Aristotle argued that knowing does not necessitate an infinite regress because some knowledge does not depend on demonstration:

Some hold that owing to the necessity of knowing the primary premises, there is no scientific knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premises. The first school, assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not know the posterior through the prior (wherein they are right, for one cannot traverse an infinite series): if on the other hand – they say – the series terminates and there are primary premises, yet these are unknowable because incapable of demonstration, which according to them is the only form of knowledge. And since thus one cannot know the primary premises, knowledge of the conclusions which follow from them is not pure scientific knowledge nor properly knowing at all, but rests on the mere supposition that the premises are true. The other party agrees with them as regards knowing, holding that it is only possible by demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal. Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premises from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.) Such, then, is our doctrine, and in addition, we maintain that besides scientific knowledge there is its original source which enables us to recognize the definitions.

— Aristotle, Posterior Analytics I.3 72b1–15

Philosophy of mind

Gilbert Ryle argues in the philosophy of mind that mind-body dualism is implausible because it produces an infinite regress of "inner observers" when trying to explain how mental states are able to influence physical states.

Zeno's paradoxes

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes

Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. It is usually assumed, based on Plato's Parmenides (128a–d), that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides' view. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one." Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point. Some of Zeno's nine surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another. Aristotle offered a refutation of some of them. Three of the strongest and most famous—that of Achilles and the tortoise, the Dichotomy argument, and that of an arrow in flight—are presented in detail below.

Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates. Some mathematicians and historians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution. Some philosophers, however, say that Zeno's paradoxes and their variations (see Thomson's lamp) remain relevant metaphysical problems. The origins of the paradoxes are somewhat unclear. Diogenes Laërtius, a fourth source for information about Zeno and his teachings, citing Favorinus, says that Zeno's teacher Parmenides was the first to introduce the paradox of Achilles and the tortoise. But in a later passage, Laërtius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees.

Paradoxes of motion

Dichotomy paradox

That which is in locomotion must arrive at the half-way stage before it arrives at the goal.

— as recounted by Aristotle, Physics VI:9, 239b10

Suppose Atalanta wishes to walk to the end of a path. Before she can get there, she must get halfway there. Before she can get halfway there, she must get a quarter of the way there. Before traveling a quarter, she must travel one-eighth; before an eighth, one-sixteenth; and so on.

The dichotomy

The resulting sequence can be represented as:

${\displaystyle \left\{\cdots ,{\frac {1}{16}},{\frac {1}{8}},{\frac {1}{4}},{\frac {1}{2}},1\right\}}$

This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.

This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can be neither completed nor begun, and so all motion must be an illusion.

This argument is called the "Dichotomy" because it involves repeatedly splitting a distance into two parts. An example with the original sense can be found in an asymptote. It is also known as the Race Course paradox.

Achilles and the tortoise

"Achilles and the Tortoise" redirects here. For other uses, see Achilles and the Tortoise (disambiguation).

Achilles and the tortoise

In a race, the quickest runner can never over­take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

— as recounted by Aristotle, Physics VI:9, 239b15

In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Suppose that each racer starts running at some constant speed, one faster than the other. After some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say 2 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise. As Aristotle noted, this argument is similar to the Dichotomy. It lacks, however, the apparent conclusion of motionlessness.

Arrow paradox

The arrow

Not to be confused with other paradoxes of the same name.

If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion.

— as recounted by Aristotle, Physics VI:9, 239b5

In the arrow paradox, Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

Whereas the first two paradoxes divide space, this paradox starts by dividing time—and not into segments, but into points.

Three other paradoxes as given by Aristotle

Paradox of place

From Aristotle:

If everything that exists has a place, place too will have a place, and so on ad infinitum.

Paradox of the grain of millet

Description of the paradox from the Routledge Dictionary of Philosophy:

The argument is that a single grain of millet makes no sound upon falling, but a thousand grains make a sound. Hence a thousand nothings become something, an absurd conclusion.

Aristotle's refutation:

Zeno is wrong in saying that there is no part of the millet that does not make a sound: for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself: for no part even exists otherwise than potentially.

Description from Nick Huggett:

This is a Parmenidean argument that one cannot trust one's sense of hearing. Aristotle's response seems to be that even inaudible sounds can add to an audible sound.

The moving rows (or stadium)

The moving rows

From Aristotle:

... concerning the two rows of bodies, each row being composed of an equal number of bodies of equal size, passing each other on a race-course as they proceed with equal velocity in opposite directions, the one row originally occupying the space between the goal and the middle point of the course and the other that between the middle point and the starting-post. This...involves the conclusion that half a given time is equal to double that time.

For an expanded account of Zeno's arguments as presented by Aristotle, see Simplicius's commentary On Aristotle's Physics.

Proposed solutions

Diogenes the Cynic

According to Simplicius, Diogenes the Cynic said nothing upon hearing Zeno's arguments, but stood up and walked, in order to demonstrate the falsity of Zeno's conclusions (see solvitur ambulando). To fully solve any of the paradoxes, however, one needs to show what is wrong with the argument, not just the conclusions. Through history, several solutions have been proposed, among the earliest recorded being those of Aristotle and Archimedes.

Aristotle

Aristotle (384 BC−322 BC) remarked that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small. Aristotle also distinguished "things infinite in respect of divisibility" (such as a unit of space that can be mentally divided into ever smaller units while remaining spatially the same) from things (or distances) that are infinite in extension ("with respect to their extremities"). Aristotle's objection to the arrow paradox was that "Time is not composed of indivisible nows any more than any other magnitude is composed of indivisibles."

Archimedes

Before 212 BC, Archimedes had developed a method to derive a finite answer for the sum of infinitely many terms that get progressively smaller. (See: Geometric series, 1/4 + 1/16 + 1/64 + 1/256 + · · ·, The Quadrature of the Parabola.) His argument, applying the method of exhaustion to prove that the infinite sum in question is equal to the area of a particular square, is largely geometric but quite rigorous. Today's analysis achieves the same result, using limits (see convergent series). These methods allow the construction of solutions based on the conditions stipulated by Zeno, i.e. the amount of time taken at each step is geometrically decreasing.

Thomas Aquinas

Thomas Aquinas, commenting on Aristotle's objection, wrote "Instants are not parts of time, for time is not made up of instants any more than a magnitude is made of points, as we have already proved. Hence it does not follow that a thing is not in motion in a given time, just because it is not in motion in any instant of that time."

Bertrand Russell

Bertrand Russell offered what is known as the "at-at theory of motion". It agrees that there can be no motion "during" a durationless instant, and contends that all that is required for motion is that the arrow be at one point at one time, at another point another time, and at appropriate points between those two points for intervening times. In this view motion is just change in position over time.

Hermann Weyl

Another proposed solution is to question one of the assumptions Zeno used in his paradoxes (particularly the Dichotomy), which is that between any two different points in space (or time), there is always another point. Without this assumption there are only a finite number of distances between two points, hence there is no infinite sequence of movements, and the paradox is resolved. According to Hermann Weyl, the assumption that space is made of finite and discrete units is subject to a further problem, given by the "tile argument" or "distance function problem". According to this, the length of the hypotenuse of a right angled triangle in discretized space is always equal to the length of one of the two sides, in contradiction to geometry. Jean Paul Van Bendegem has argued that the Tile Argument can be resolved, and that discretization can therefore remove the paradox.

Henri Bergson

An alternative conclusion, proposed by Henri Bergson in his 1896 book Matter and Memory, is that, while the path is divisible, the motion is not. In this argument, instants in time and instantaneous magnitudes do not physically exist. An object in relative motion cannot have an instantaneous or determined relative position, and so cannot have its motion fractionally dissected.

Peter Lynds

In 2003, Peter Lynds put forth a very similar argument: all of Zeno's motion paradoxes are resolved by the conclusion that instants in time and instantaneous magnitudes do not physically exist.  Lynds argues that an object in relative motion cannot have an instantaneous or determined relative position (for if it did, it could not be in motion), and so cannot have its motion fractionally dissected as if it does, as is assumed by the paradoxes. For more about the inability to know both speed and location, see Heisenberg uncertainty principle.

Nick Huggett

Nick Huggett argues that Zeno is assuming the conclusion when he says that objects that occupy the same space as they do at rest must be at rest.

Paradoxes in modern times

Infinite processes remained theoretically troublesome in mathematics until the late 19th century. With the epsilon-delta definition of limit, Weierstrass and Cauchy developed a rigorous formulation of the logic and calculus involved. These works resolved the mathematics involving infinite processes.

While mathematics can calculate where and when the moving Achilles will overtake the Tortoise of Zeno's paradox, philosophers such as Kevin Brown and Francis Moorcroft claim that mathematics does not address the central point in Zeno's argument, and that solving the mathematical issues does not solve every issue the paradoxes raise.

Popular literature often misrepresents Zeno's arguments. For example, Zeno is often said to have argued that the sum of an infinite number of terms must itself be infinite–with the result that not only the time, but also the distance to be travelled, become infinite. However, none of the original ancient sources has Zeno discussing the sum of any infinite series. Simplicius has Zeno saying "it is impossible to traverse an infinite number of things in a finite time". This presents Zeno's problem not with finding the sum, but rather with finishing a task with an infinite number of steps: how can one ever get from A to B, if an infinite number of (non-instantaneous) events can be identified that need to precede the arrival at B, and one cannot reach even the beginning of a "last event"?

A humorous take is offered by Tom Stoppard in his 1972 play Jumpers, in which the principal protagonist, the philosophy professor George Moore, suggests that according to Zeno's paradox, Saint Sebastian, a 3rd Century Christian saint martyred by being shot with arrows, died of fright.

Debate continues on the question of whether or not Zeno's paradoxes have been resolved. In The History of Mathematics: An Introduction (2010) Burton writes, "Although Zeno's argument confounded his contemporaries, a satisfactory explanation incorporates a now-familiar idea, the notion of a 'convergent infinite series.'"

Bertrand Russell offered a "solution" to the paradoxes based on the work of Georg Cantor, but Brown concludes "Given the history of 'final resolutions', from Aristotle onwards, it's probably foolhardy to think we've reached the end. It may be that Zeno's arguments on motion, because of their simplicity and universality, will always serve as a kind of 'Rorschach image' onto which people can project their most fundamental phenomenological concerns (if they have any)."

A similar ancient Chinese philosophic consideration

Ancient Chinese philosophers from the Mohist School of Names during the Warring States period of China (479-221 BC) developed equivalents to some of Zeno's paradoxes. The scientist and historian Sir Joseph Needham, in his Science and Civilisation in China, describes an ancient Chinese paradox from the surviving Mohist School of Names book of logic which states, in the archaic ancient Chinese script, "a one-foot stick, every day take away half of it, in a myriad ages it will not be exhausted." Several other paradoxes from this philosophical school (more precisely, movement) are known, but their modern interpretation is more speculative.

Quantum Zeno effect

Main article: Quantum Zeno effect

In 1977, physicists E. C. George Sudarshan and B. Misra discovered that the dynamical evolution (motion) of a quantum system can be hindered (or even inhibited) through observation of the system. This effect is usually called the "quantum Zeno effect" as it is strongly reminiscent of Zeno's arrow paradox. This effect was first theorized in 1958.

Zeno behaviour

In the field of verification and design of timed and hybrid systems, the system behaviour is called Zeno if it includes an infinite number of discrete steps in a finite amount of time. Some formal verification techniques exclude these behaviours from analysis, if they are not equivalent to non-Zeno behaviour. In systems design these behaviours will also often be excluded from system models, since they cannot be implemented with a digital controller.

Lewis Carroll and Douglas Hofstadter

What the Tortoise Said to Achilles, written in 1895 by Lewis Carroll, was an attempt to reveal an analogous paradox in the realm of pure logic. If Carroll's argument is valid, the implication is that Zeno's paradoxes of motion are not essentially problems of space and time, but go right to the heart of reasoning itself. Douglas Hofstadter made Carroll's article a centrepiece of his book Gödel, Escher, Bach: An Eternal Golden Braid, writing many more dialogues between Achilles and the Tortoise to elucidate his arguments. Hofstadter connects Zeno's paradoxes to Gödel's incompleteness theorem in an attempt to demonstrate that the problems raised by Zeno are pervasive and manifest in formal systems theory, computing and the philosophy of mind.